Finite Group Databasebeta

← #14518134

Subgroups — #14518134

Order 1944.

266 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11757776C211yesmaximal, characteristic, complemented
2C3×A4×C3⋊D3C311yesmaximal, characteristic
3D3×C9⋊A4—31nomaximal
4C22×(C3⋊D3)⋊C9C311yesmaximal, characteristic, complemented
5(C3⋊D3)⋊(C22⋊C9)C312yesmaximal, complemented
6#92259—41nomaximal
7C33×A4C2×C311yescharacteristic
8C3×C9⋊A4—21no—
9C3×C9⋊A4D311yescharacteristic, complemented
10C22×C32⋊C9C2×C311yescharacteristic, complemented
11C2×(C3⋊D3)⋊C9—31no—
12C2×(C3⋊D3)⋊C9—31no—
13C32⋊(C22⋊C9)C2×C312yescomplemented
14(C3×A4)⋊C9—21no—
15(C3×A4)⋊C9—22no—
16#6891—41noSylow
17C22×C3×C3⋊D3C3211yescharacteristic
18A4×C3⋊D3—31no—
19C3×D3×A4—31no—
20C3×D3×A4—91no—
21C22×D3×C9—31no—
22C2×C9⋊A4—91no—
23D3×C22⋊C9—32no—
24C32×C3⋊D3—41no—
25D3×3−1+2—121no—
26C2×C32⋊C9—31no—
27(C3⋊D3)⋊C9—31no—
28(C3⋊D3)⋊C9—42no—
29(C3⋊D3)⋊C9A411yescharacteristic, complemented
30C22×C33C2×C3211yescharacteristic
31C2×C3×C3⋊D3—31no—
32C2×C3×C3⋊D3—31no—
33C32×A4—21no—
34C32×A4—31no—
35C32×A4—31no—
36C32×A4—63no—
37C32×A4—61no—
38C32×A4—61no—
39C32×A4C3×D311yescharacteristic
40C22×C3×C9—21no—
41C22×C3×C9C3×D311yescharacteristic, complemented
42C2×D3×C9—91no—
43C2×D3×C9—91no—
44C3×C22⋊C9—22no—
45C3×C22⋊C9C3×D312yescomplemented
46C9⋊A4—31no—
47C9⋊A4—61no—
48C9⋊A4—62no—
49C9⋊A4—61no—
50C34—41no—
51C3×3−1+2—41no—
52C3×3−1+2—81no—
53C32⋊C9—42no—
54C32⋊C9—82no—
55C32⋊C9—81no—
56C32⋊C9C2×A411yescharacteristic, complemented
57C22×C3⋊D33−1+211yescharacteristic, complemented
58C22×C3×D3—31no—
59C22×C3×D3—91no—
60C2×C3×A4—91no—
61D3×A4—91no—
62D3×A4—93no—
63C23×C9—91no—
64C2×C22⋊C9—92no—
65C2×C33—31no—
66C3×C3⋊D3—31no—
67C3×C3⋊D3—121no—
68C3×C3⋊D3C3×A411yescharacteristic
69C32×D3—121no—
70C32×D3—361no—
71C2×3−1+2—361no—
72C2×C3×C9—31no—
73C2×C3×C9—61no—
74D3×C9—31no—
75D3×C9—91no—
76D3×C9—122no—
77C22×C32—21no—
78C22×C32—31no—
79C22×C32—61no—
80C22×C32C2×3−1+211yescharacteristic, complemented
81C22×C32C32×D311yescharacteristic
82C2×C3⋊D3—31no—
83C2×C3⋊D3—31no—
84C2×C3×D3—91no—
85C2×C3×D3—91no—
86C2×C3×D3—271no—
87C2×C3×D3—271no—
88C3×A4—23no—
89C3×A4—21no—
90C3×A4—33no—
91C3×A4—31no—
92C3×A4—63no—
93C3×A4—61no—
94C3×A4—61no—
95C3×A4—63no—
96C3×A4—63no—
97C3×A4—61no—
98C3×A4—61no—
99C3×A4—63no—
100C3×A4(C3⋊D3)⋊C311yescharacteristic
101C22×C9—31no—
102C22×C9—61no—
103C22×C9—271no—
104C22×C9—271no—
105C22⋊C9—32no—
106C22⋊C9—62no—
107C33—41no—
108C33—81no—
109C33—121no—
110C33—121no—
111C33—241no—
112C33—241no—
113C33—243no—
114C33C2×C3×A411yescharacteristic
1153−1+2—121no—
1163−1+2—241no—
1173−1+2—241no—
1183−1+2—242no—
119C3×C9—21no—
120C3×C9—42no—
121C3×C9—82no—
122C3×C9D3×A411yescharacteristic, complemented
123C23×C3—91no—
124C22×D3—31no—
125C22×D3—91no—
126C2×A4—271no—
127C2×C32—31no—
128C2×C32—31no—
129C2×C32—61no—
130C2×C32—91no—
131C2×C32—181no—
132C2×C32—361no—
133C3⋊D3—31no—
134C3⋊D3C9⋊A411yescharacteristic, complemented
135C3×D3—31no—
136C3×D3—91no—
137C3×D3—91no—
138C3×D3—271no—
139C3×D3—361no—
140C3×D3—363no—
141C2×C9—91no—
142C2×C9—91no—
143C2×C9—181no—
144C2×C9—271no—
145C2×C9—362no—
146C22×C3—21no—
147C22×C3—31no—
148C22×C3—61no—
149C22×C3—271no—
150C22×C3—271no—
151C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
152C22×C3D3×3−1+211yescharacteristic
153C2×D3—91no—
154C2×D3—91no—
155C2×D3—271no—
156C2×D3—271no—
157A4—31no—
158A4—63no—
159A4—61no—
160C32—21no—
161C32—31no—
162C32—41no—
163C32—61no—
164C32—83no—
165C32—81no—
166C32—123no—
167C32—121no—
168C32—241no—
169C32—241no—
170C32—243no—
171C32—243no—
172C32—243no—
173C32—243no—
174C32—241no—
175C32—241no—
176C32C2×C9⋊A411yescharacteristic, complemented
177C32C3×D3×A411yescharacteristic
178C9—31no—
179C9—61no—
180C9—122no—
181C9—242no—
182C23—91noSylow
183C2×C3—31no—
184C2×C3—31no—
185C2×C3—61no—
186C2×C3—91no—
187C2×C3—91no—
188C2×C3—181no—
189C2×C3—271no—
190C2×C3—1081no—
191D3—31no—
192D3—91no—
193D3—91no—
194D3—271no—
195C22—271no—
196C22—271no—
197C22#9225911yescharacteristic, complemented
198C3—21no—
199C3—31no—
200C3—61no—
201C3—121no—
202C3—243no—
203C3—241no—
204C3D3×C9⋊A411yescharacteristic
205C3A4×(C3⋊D3)⋊C311yescharacteristic
206C2—31no—
207C2—91no—
208C2—271no—
subgroupG/H
center, hypercenterC3A4×(C3⋊D3)⋊C3
commutator, cosocleC22×C33C2×C32
FrattiniC32C3×D3×A4
FittingC22×C32⋊C9C2×C3
socleC22×C32C32×D3
prime radicalC3×A4×C3⋊D3C3
hypocenterC22×C32C2×3−1+2
LCSG ▷ C22×C33 ▷ C22×C32
UCSC1 ◁ C3

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #11757776C2semidirect
4. C22×(C3⋊D3)⋊C9C3semidirect
5. (C3⋊D3)⋊(C22⋊C9)C3semidirect
9. C3×C9⋊A4D3semidirect
10. C22×C32⋊C9C2×C3semidirect
13. C32⋊(C22⋊C9)C2×C3semidirect
29. (C3⋊D3)⋊C9A4semidirect
41. C22×C3×C9C3×D3semidirect
45. C3×C22⋊C9C3×D3semidirect
56. C32⋊C9C2×A4semidirect
57. C22×C3⋊D33−1+2semidirect
80. C22×C32C2×3−1+2semidirect
122. C3×C9D3×A4semidirect
134. C3⋊D3C9⋊A4semidirect
176. C32C2×C9⋊A4semidirect
197. C22#92259semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117577762
C3×A4×C3⋊D33
D3×C9⋊A43
C22×(C3⋊D3)⋊C93
(C3⋊D3)⋊(C22⋊C9)3
#922594